Fair risk optimization of distributed systems

The paper provides a framework for the assessment and optimization of the total risk of complex distributed systems. The framework takes into account the risk of each agent, which may arise from heterogeneous sources, as well as the risk associated with the efficient operation of the system as a whole. The challenges posed by this task are associated with the lack of additivity of risk, the need to evaluate the risk of every agent (unit) using confidential or proprietary information, and the requirement of fair risk allocation to agents (units). We analyze systemic risk measures that are based on a sound axiomatic foundation while at the same time facilitate risk-averse sequential decision-making by distributed numerical methods, which allow the agents to operate autonomously with minimal exchange of information. We formulate a two-stage decision problem for a distributed system using systemic measures of risk and devise a decomposition method for solving the problem. The method is applied to a disaster management problem. We have paid attention to maintain fair risk allocation to all areas in the course of the relief operation. Our numerical results show the efficiency of the proposed methodology.